Rule talk:Hutton32
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The Hutton32 rule was created as a rule tree mainly for test purposes. It's considerably more compact in rule-table format:
@RULE Hutton32
# Hutton32 - a modified version of von Neumann's cellular automaton.
# Tim Hutton <tim.hutton@gmail.com>
#
# Motivation: In the original von Neumann transition rules, lines of
# transmission states can extend themselves by writing out binary
# signal trains, e.g. 10000 for extend with a right-directed ordinary
# transmission state (OTS). But for construction, a dual-stranded
# construction arm (c-arm) is needed, simply because the arm must be
# retracted after each write. I noticed that there was room to add the
# needed write-and-retract operation by modifying the transition rules
# slightly. This allows the machine to be greatly reduced in size and
# speed of replication.
#
# Another modification was made when it was noticed that the
# construction could be made rotationally invariant simply by basing
# the orientation of the written cell on the orientation of the one
# writing it. Instead of "write an up arrow" we have "turn left". This
# allows us to spawn offspring in different directions and to fill up
# the space with more and more copies in a manner inspired by
# Langton's Loops.
#
# Having modified the von Neumann CA transition rules, a new form of
# self-replicator becomes possible, one that replicates much faster
# and exhibits exponential growth in the initial stages.
#
# A single OTS line can now act as a c-arm in any direction. Below are
# the signal trains:
#
# 100000 : move forward (write an OTS arrow in the same direction)
# 100010 : turn left
# 10100 : turn right
# 100001 : write a forward-directed OTS and retract
# 100011 : write a left-directed OTS and retract
# 10011 : write a reverse-directed OTS and retract
# 10101 : write a right-directed OTS and retract
# 101101 : write a forward-directed STS and retract
# 110001 : write a left-directed STS and retract
# 110101 : write a reverse-directed STS and retract
# 111001 : write a right-directed STS and retract
# 1111 : write a confluent state and retract
# 101111 : retract
#
# Achieving these features without adding new states required making
# some slight changes elsewhere, though hopefully these don't affect
# the computation- or construction-universality of the CA. The most
# important effects are listed here:
#
# 1) OTS's cannot destroy special transmission states (STS's). This
# functionality was used in von Neumann's construction and read-
# write arms but isn't needed for the logic organs, as far as I
# know. The opposite operation is still enabled.
# 2) STS lines can only construct one cell type: an OTS in the forward
# direction. Some logic organs will need to be redesigned.
#
# Under this modified JvN rule, a self-replicator can be much smaller,
# consisting only of a tape contained within a repeater-emitter loop.
# One early example consisted of 5521 cells in total, and replicates
# in 44,201 timesteps, compared with 8 billion timesteps for the
# smallest known Nobili32 replicator. This became possible because the
# construction process runs at the same speed as a moving signal,
# allowing the tape to be simply stored in a repeater-emitter loop.
# The machine simply creates a loop of the right size (by counting
# tape circuits) before allowing the tape contents to fill up their
# new home.
#
# The rotational invariance allows the machine to make multiple copies
# oriented in different directions. The population growth starts off
# as exponential but soons slows down as the long tapes obstruct the
# new copies.
#
# Some context for these modifications to von Neumann's rule table:
# Codd simplified vN's CA to a rotationally-invariant 8 states.
# Langton modified this to make a self-replicating repeater-emitter,
# his 'loops'. Other loops were made by Sayama, Perrier, Tempesti,
# Byl, Chou-Reggia, and others. So there are other CA derived from
# vN's that support faster replication than that achieveable here, and
# some of them retain the computation- and construction-universality
# that von Neumann was considering. Our modifications are mostly a
# historical exploration of the possibility space around vN's CA, to
# explore the questions of why he made the design decisions he did.
# In particular, why didn't von Neumann design for a tape loop stored
# within a repeater-emitter? It would have made his machine much
# simpler from the beginning. Why didn't he consider write-and-
# retraction instead of designing a complicated c-arm procedure? Of
# course this is far from criticism of vN - his untimely death
# interrupted his work in this area.
#
# Some details of the modifications are given below:
#
# The transition rules are as in Nobili32 (or JvN29), except the
# following:
# 1) The end of an OTS wire, when writing a new cell, adopts one of
# two states: excited OTS and excited STS, standing for bits 1 and
# 0 respectively. After writing the cell reverts to being an OTS.
# 2) A sensitized cell that is about to revert to an arrow bases its
# direction upon that of the excited arrow that is pointing to it.
# 3) A TS 'c', with a sensitized state 's' on its output that will
# become an OTS next (based on the state of 'c'), reverts to the
# ground state if any of 'c's input is 1, else it quiesces.
# 4) A TS 'c', with a sensitized state 's' on its output that will
# become a confluent state next (based on the state of 'c'),
# reverts to the first sensitized state S is any of 'c's input is
# one, else it reverts to the ground state.
# 5) A TS 'c', with an STS on its output, reverts to the ground state
# if any of 'c's input is 1.
#
# The body of the machine looks fiddly but it only does these things:
# 1) detect a unique mark on the tape as it goes round
# 2) starts and stops a 6-period pulser
# 3) codes for: extend, turn left, turn left, extend some more
# 4) counts when 3 tape marks have gone past, and switches coder
# 5) when finished writing an empty tape of the right length,
# divert the tape to copy itself into the new holder
# 6) after the tape is copied across, it separates itself from its
# old tape to prevent infection spreading from multiple copies.
#
# Automatically produced file from a previous implementation, produced using
# bottom-up merging of the transition rules.
#
# Where a variable appears more than once in a rule, it is constrained
# to have the same value each time.
# e.g. for var a={1,2}: 1,a,a,0,2,0 is 2 rules, not 4
#
# rules: 296
#
# Golly rule-table format.
# Each rule: C,N,E,S,W,C'
#
# Default for transitions not listed: no change
#
n_states:32
neighborhood:vonNeumann
symmetries:none
var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31}
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var o={15,23}
var p={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,29,30,31}
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var B={5,8,17,18,19,20}
var C={0,1,2,3,4,6,7,9,10,11,12,13,14,15,16,21,22,23,25,26,27,28,29,30,31}
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var I={0,1,2,3}
var J={4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,24,25,26,27,28,29,30,31}
var K={4,8,17,18,19,20}
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var R={22,27,28,30,31}
var S={17,18,19,20,21}
var T={17,18,19,20,22}
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var V={23,27,28,29,31}
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var aa={1,2,3,4}
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var ac={5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31}
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var ag={0,1,2,3,4,5,6,7,8,9,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31}
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var ak={9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31}
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1,e,f,g,h,2
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2,a,b,14,h,5
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11,y,F,z,B,0
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14,7,F,z,v,0
14,7,n,r,s,1
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18,e,f,g,P,22
18,e,f,R,v,22
18,e,V,z,v,22
19,e,f,R,h,23
19,e,V,z,h,23
19,U,F,z,h,23
20,e,f,g,P,24
20,e,V,g,v,24
20,U,F,g,v,24
21,p,0,r,w,17
21,W,X,Y,Z,17
21,a,aa,b,13,13
21,a,aa,14,h,13
21,e,ab,g,9,9
21,a,ac,b,13,0
21,e,ab,10,ad,9
21,a,ac,14,h,0
21,H,ae,z,v,17
21,0,9,10,af,17
21,12,ab,ag,ad,9
21,16,aa,g,h,13
21,16,ac,g,h,0
22,0,n,r,w,18
22,ah,ai,Y,Z,18
22,aa,a,b,13,14
22,aa,a,14,h,14
22,aa,15,g,h,14
22,ab,f,g,9,10
22,aj,a,b,13,0
22,ab,f,10,ad,10
22,aj,a,14,h,0
22,ab,11,ag,ad,10
22,aj,15,g,h,0
22,ak,F,z,v,18
22,9,0,10,af,18
23,W,ai,Y,h,19
23,H,F,z,al,19
23,e,f,10,ab,11
23,p,n,r,0,19
23,a,b,14,aa,15
23,a,b,14,am,0
23,0,11,an,al,19
23,e,11,ag,ab,11
23,0,D,ao,0,19
23,a,15,g,aa,15
23,a,15,g,am,0
23,12,ap,ag,ab,11
23,16,f,g,aa,15
23,16,f,g,am,0
24,p,n,0,w,20
24,W,ai,aq,Z,20
24,a,b,aa,13,16
24,e,f,ab,9,12
24,a,b,ar,13,0
24,H,F,as,v,20
24,e,11,ab,ad,12
24,0,11,9,af,20
24,a,15,aa,h,16
24,a,15,ar,h,0
24,12,ap,ab,ad,12
24,16,f,aa,h,16
24,16,f,ar,h,0
at,au,av,aw,13,26
at,au,av,14,ax,26
at,au,15,ay,ax,26
at,az,au,aw,13,26
at,az,au,14,ax,26
at,aA,aB,aC,13,26
aD,aA,aB,aE,13,29
at,aA,aB,14,aF,26
aG,aA,aB,14,aH,30
aI,aA,aB,14,13,31
aD,aA,aJ,aK,13,29
aG,aA,aL,14,aM,30
at,az,15,au,aN,26
at,aA,15,aK,aF,26
aD,aA,15,aK,aH,29
aD,aA,15,aE,aM,29
at,az,15,aO,aP,26
aI,aA,15,14,aM,31
at,az,19,aQ,13,26
at,az,19,14,aR,26
aD,aS,aB,aK,13,29
aG,aT,aB,14,aM,30
aD,aS,15,aK,aM,29
at,16,au,ay,ax,26
at,16,aU,au,aN,26
at,16,aB,aK,aF,26
aG,16,aB,aK,aH,30
aI,16,aB,aK,13,31
aG,16,aB,aE,aM,30
at,16,aU,aO,aP,26
aG,16,aL,aK,aM,30
at,16,aV,aK,aP,26
aI,16,15,aK,aM,31
at,16,aV,aO,aM,26
at,20,aB,aQ,13,26
at,20,aB,14,aR,26
at,20,15,aK,aP,26
at,20,15,aO,aM,26
at,20,19,aK,13,26
at,20,19,14,aM,26
aW,l,k,j,i,27
26,aX,av,aw,13,28
aW,p,n,10,w,27
26,aX,av,14,ax,28
aW,p,n,aw,9,27
aW,p,11,aw,aN,27
26,0,11,14,aY,27
26,aX,15,ay,ax,28
26,0,15,ao,9,27
26,0,15,10,aY,27
aW,12,av,aw,aN,27
26,12,0,14,aY,27
26,16,aZ,ay,ax,28
ba,l,k,j,i,25
27,p,n,10,w,25
27,p,n,aw,9,25
27,p,11,aw,aN,25
27,0,11,14,aY,25
27,0,15,ao,9,25
27,0,15,10,aY,25
27,aA,aB,14,bb,26
27,aA,aB,18,13,26
27,aA,15,aK,bb,26
27,aA,15,aO,aM,26
27,aA,19,aK,13,26
27,aA,19,14,aM,26
27,12,av,aw,aN,25
27,12,0,14,aY,25
27,16,aB,aK,bb,26
27,16,aB,aO,aM,26
27,16,aV,aK,aM,26
27,20,aB,aK,13,26
27,20,aB,14,aM,26
27,20,15,aK,aM,26
bc,p,k,14,i,30
bd,p,n,14,13,31
bd,p,15,14,i,31
bc,16,k,j,i,30
bd,16,n,j,13,31
bd,16,15,j,i,31
be,l,n,j,13,29
be,l,15,j,i,29